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Applied Optics

Engineering the nonlinear phase shift with multistage autoregressive moving-average optical filters

Yan Chen, Geeta Pasrija, Behrouz Farhang‐Boroujeny, Steve Blair

Published May 1, 2005• 3 citations
Publisher

Abstract

We propose and demonstrate the application of concepts from digital filter design in order to optimize artificial optical resonant structures to produce a nearly ideal nonlinear phase shift response. Multistage autoregressive moving average (ARMA) optical filters (ring-resonator-based Mach-Zehnder interferometer lattices) are designed and studied. The filter group delay is used as a measure instead of finesse or quality factor to study the nonlinear sensitivity for multiple resonances. The nonlinearity of a four-stage ARMA filter is 17 times higher than that of the intrinsic material of the same group delay. We demonstrate that the nonlinear sensitivity can be increased within constant bandwidth by allocating more in-band phase or by using higher-order filter structures and that the nonlinear sensitivity enhancement improves with increasing group delay. We also investigate methods to precompensate the nonlinear response to reduce the occurrence of optical bistabilities. The effect of optical loss, including linear absorption and two-photon absorption, is discussed in postanalysis. In addition, we discuss how the improvement in nonlinear response scales with respect to various filter parameters.

DOI
10.1364/ao.44.002564

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We propose and demonstrate the application of concepts from digital filter design in order to optimize artificial optical resonant structures to produce a nearly ideal nonlinear phase shift response. Multistage autoregressive moving average (ARMA) optical filters (ring-resonator-based Mach-Zehnder interferometer lattices) are designed and studied. The filter group delay is used as a measure instead of finesse or quality factor to study the nonlinear sensitivity for multiple resonances. The nonlinearity of a four-stage ARMA filter is 17 times higher than that of the intrinsic material of the same group delay. We demonstrate that the nonlinear sensitivity can be increased within constant bandwidth by allocating more in-band phase or by using higher-order filter structures and that the nonlinear sensitivity enhancement improves with increasing group delay. We also investigate methods to precompensate the nonlinear response to reduce the occurrence of optical bistabilities. The effect of optical loss, including linear absorption and two-photon absorption, is discussed in postanalysis. In addition, we discuss how the improvement in nonlinear response scales with respect to various filter parameters.
In this paper, we propose and demonstrate the application of concepts from digital filter design to optimize artificial optical resonant structures to produce a nearly ideal nonlinear phase shift response. Multi-stage autoregressive moving average (ARMA) optical filters (ring resonator based Mach-Zehnder interferometer lattices) are designed and studied. The filter group delay is used as an alternate measure instead of finesse or quality factor to study the nonlinear sensitivity for multiple resonances. The nonlinearity of a 4-stage ARMA filter is 17 times higher than that of the intrinsic material. We demonstrate that the nonlinear sensitivity can be increased within the same bandwidth by allocating more in-band phase or using higher-order filter structures and that the nonlinear enhancement improves with increasing group delay. We also investigate some possible ways to pre-compensate the nonlinear response to reduce the occurrence of optical bistabilities. The impact of optical loss, including linear absorption and two-photon absorption, and fabrication tolerance are discussed in post-analysis.
We study pulse propagation in the slow-light regime with positive and negative group delays in auto-regressive moving average (ARMA) filters, including the ring-enhanced Mach-Zehnder interferometer (REMZI) and side-coupled integrated spaced sequence of resonators (SCISSOR) optical architectures. Both architectures are optimized to maximize the delay-bandwidth product for a fixed output pulse-distortion level. In the negative-group-delay regime, absorption is incorporated in the rings. The REMZI architecture has the highest delay-bandwidth product in both the positive and negative-group-delay regimes due to greater efficiency in incorporating filter phase within the passband. We also explore the effects of pulse shape in the lossy regime and the limitations it poses in the amount of pulse advancement that is usable for practical applications.
Under the constraint of fixed pulse distortion, we study the bandwidth-delay product and nonlinear phase shift performance of coupled-resonator slow-light waveguides with designs that produce maximally-flat transmission and maximally-flat group delay responses. Even though improvement in bandwidth-delay product can be obtained with increasing number of resonators, the nonlinear response fails to improve beyond a certain number of resonators due to the increased filter bandwidth necessary to maintain a fixed pulse distortion. However, as expected, the nonlinear response improves with resonator finesse and degrades with resonator loss.
Photonic microring resonators are used in a variety of chip-integrated sensing applications where they allow one to measure transmission intensity changes upon external signals with a sensitivity that scales linearly with the Q factor. In this work, we suggest exploiting the nonlinear self-phase-modulation effect to increase the overall sensitivity by an additional gain factor appearing when the operational point of the nonlinear resonator is chosen just at the crossover from the monostable to the bistable regime. We present the theoretical idea together with a first proof of concept experiment displaying a gain factor of 22 on a chip-integrated silicon-nitride resonator.
Optical nonlinear processes in linearly uncoupled resonators are being actively studied as a convenient way to engineer and control the generation of non-classical light. In these structures, one can take advantage of the independent combs of resonances of two linearly uncoupled ring resonators for field enhancement, with the phase-matching condition being significantly relaxed compared to a single resonator. However, previous implementations of this approach have shown a limited operational bandwidth along with a significant reduction of the generation efficiency. Here, we experimentally demonstrate that a Mach–Zehnder interferometer can be used to effectively linearly uncouple two resonators and, at the same time, allows for their efficient nonlinear coupling. We demonstrate that this structure can lead to an unprecedented control over the rings' interaction and can operate over more than 160 nm, covering the S-, C-, and L-telecom bands. In addition, we show that the photon pair generation efficiency is increased by a factor of four with respect to previous implementations.
To enhance the phase sensitivity of Mach–Zehnder interferometers, we use a tunable phase shift before the light beams are injected into the interferometer. The analytical result of the optimal phase shift is obtained, which only depends on the initial input states. For a non-zero optimal phase shift, the phase sensitivity of the interferometers in the output ports is always enhanced. We can achieve this enhancement for most states, including entangled and mixed states. The optimal phase shift is exhibited in three examples. Compared to previous methods, this scheme provides a general way to improve phase sensitivity and could find wide applications in optical phase estimations.